But quitting the 28-member bloc would send prices in the shops rocketing and risk a spike in inflation, job losses and a plunging pound, leading high street bosses have claimed.

Former chiefs of Tesco, Sainsbury's, Marks & Spencer and B&Q warned that leaving could have a "catastrophic" impact on the economy.

Leave campaigners claimed that allowing countries on the path to EU membership to join was "dangerous" and made the country "less safe".

Accession of Turkey, Albania, Montenegro, Serbia and Macedonia will bring 12,726,000 guns into the single market, Vote Leave said.

It also also pointed to United Nations figures that showed there were more than twice as many criminal prosecutions in Turkey as in the UK in 2013 - 3.5 million compared with1.5 million.

And the Brexit camp used Romanian and Bulgarian migration rates to predict that around 142,000 Turkish citizens a year could head to the UK if the country gains full EU membership.

High Turkish birth rates - 17.4 per 1,000 people compared to 12.1 in Britain in 2014 - could cost the NHS £400 million in maternity services in a decade, it claims.

Ms Mordaunt said: "A remain vote in this referendum is a vote to allow people from Albania, Macedonia, Montenegro, Serbia and Turkey to move here freely when they join the EU soon.

"Many of these countries have high crime rates, problems with gangs and terror cells as well as challenging levels of poverty. What's more, we are currently sending these countries £2 billion to speed up the process of them joining the EU.

"I believe that this is dangerous and it will make us less safe. That's why the safer option in this referendum is to Vote Leave and take back control."

He said: "Vote Leave are desperate to avoid experts' warnings that leaving Europe would send Britain back to recession, and so are making arguments that are absurd and untrue. Even Boris Johnson has said that Turkey joining the EU is 'simply not on the cards'.

"Turkey simply will not join the EU any time soon. In 30 years of negotiations, they have completed just one of the 35 tests they need to fulfil to apply to join. Every EU country, including Britain, has a veto on any new country joining. And if they do join in the distant future, our government will have the power to impose transitional controls to restrict immigration from Turkey.

"Leaving Europe's free trade single market of 500 million people will hit our economy to the tune of £4,300 a year for the average household. And pulling out of EU co-operation on policing and border control will make our country less safe. Britain is stronger in Europe, and leaving would be a risk we cannot afford to take."

In an article for the Mail on Sunday they said: "We believe an exit could be catastrophic for the consumer recovery on which so much of our economic stability depends.

"It is impossible to see how there could be an exit without an impact on prices and inflation. The unintended consequences of a Leave vote and the uncertainty it would create would be a massive shock to the system."

Other EU countries could "exploit" exit negotiations for their own benefit, they warned.

"It's difficult to imagine that French farmers will continue to allow British lamb to be freely imported," they said.

Prime Minister David Cameron backed the high street bosses, telling The Mail on Sunday: "This is a stark warning from our most successful retailers about the risks Britain faces if we take a leap in the dark and leave the EU.

"They are absolutely clear that millions of families will face higher prices in the shops."

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